Relaxed Stability Criteria for Time-Delay Systems: A Novel Quadratic Function Convex Approximation Approach

Shenquan Wang; Wenchengyu Ji; Yulian Jiang; Yanzheng Zhu; Jian Sun

doi:10.1109/JAS.2023.123735

Volume 11 Issue 4

Apr. 2024

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2024 > 11(4): 996-1006

S. Wang, W. Ji, Y. Jiang, Y. Zhu, and J. Sun, “Relaxed stability criteria for time-delay systems: A novel quadratic function convex approximation approach,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 4, pp. 996–1006, Apr. 2024. doi: 10.1109/JAS.2023.123735

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S. Wang, W. Ji, Y. Jiang, Y. Zhu, and J. Sun, “Relaxed stability criteria for time-delay systems: A novel quadratic function convex approximation approach,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 4, pp. 996–1006, Apr. 2024. doi: 10.1109/JAS.2023.123735

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Relaxed Stability Criteria for Time-Delay Systems: A Novel Quadratic Function Convex Approximation Approach

doi: 10.1109/JAS.2023.123735

Funds: This work was supported in part by the National Natural Science Foundation of China (62273058, U22A2045), the Key Science and Technology Projects of Jilin Province (20200401075GX), and the Youth Science and Technology Innovation and Entrepreneurship Outstanding Talents Project of Jilin Province (20230508043RC)

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Author Bio:
Shenquan Wang received the Ph.D. degree in control science and engineering from Northeastern University in 2014. From November 2014 to July 2017, he was a Postdoctoral Research Associate with the State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences. From 2021 to 2022, he was an Academic Visitor with the Department of Automation, Tsinghua University. He is currently a Professor with the College of Electrical and Electronic Engineering, Changchun University of Technology. His main research interests include robust stability theory, adaptive/distributed control, and complex systems security and reliability

Wenchengyu Ji received the B.S. degree from Wuhan University in 2016, and the M.S. degree from the College of Electrical and Electronic Engineering, Changchun University of Technology in 2019. He is currently a Ph.D. candidate in mechanical engineering at the College of Electrical and Electronic Engineering, Changchun University of Technology. His current research interests include sampled-data control and stability for time-delay systems

Yulian Jiang received the Ph.D. degree in control science and engineering from Northeastern University in 2014. She is currently a Professor with the College of Electrical and Electronic Engineering, Changchun University of Technology. Her research interests cover coordination control for multiagent systems, and intelligent control theory and application

Yanzheng Zhu (Senior Member, IEEE) received the Ph.D. degree in control science and engineering from the Harbin Institute of Technology in January 2016. From 2013 to 2015, he was a joint Ph.D. student with the Department of Electrical and Computer Engineering, Ohio State University, USA. From 2016 to 2018, he was a Postdoctoral Researcher with the College of Electrical Engineering and Automation, Shandong University of Science and Technology. From 2017 to 2019, he was a Research Fellow with the School of Computing, Engineering and Mathematics, Western Sydney University, Australia. From 2019 to 2022, he was a Full Professor with the College of Mechanical Engineering and Automation, Huaqiao University. He is currently a Full Professor with the College of Electrical Engineering and Automation, Shandong University of Science and Technology. His research interests include nondeterministic switched systems, fault diagnosis and tolerant control, and their applications.Prof. Zhu serves as an Associate Editor for IEEE Control Systems Letters, and was a Guest Editor for European Journal of Control

Jian Sun (Senior Member, IEEE) received the B.S. degree in electrical engineering and automation from the Department of Automation and Electric Engineering, Jilin Institute of Technology in 2001, the M.S. degree in mechanical and electronic engineering from the Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences (CAS) in 2004, and the Ph.D. degree in control theory and control engineering from the Institute of Automation, CAS in 2007. He was a Research Fellow with the Faculty of Advanced Technology, University of Glamorgan, UK, from 2008 to 2009. He was a Postdoctoral Research Fellow with the Beijing Institute of Technology from 2007 to 2010. In 2010, he joined the School of Automation, Beijing Institute of Technology, where he has been a Professor, since 2013. His research interests include networked control systems, time-delay systems, and security of cyber-physical systems.Dr. Sun is an Editorial Board Member for the IEEE Transactions on Systems, Man and Cybernetics: Systems, the Journal of Systems Science and Complexity, and Acta Automatica Sinica
Corresponding author: Jian Sun, e-mail: sunjian@bit.edu.cn
Received Date: 2023-05-08
Accepted Date: 2023-06-12

Available Online: 2023-09-28

Abstract

Abstract

This paper develops a quadratic function convex approximation approach to deal with the negative definite problem of the quadratic function induced by stability analysis of linear systems with time-varying delays. By introducing two adjustable parameters and two free variables, a novel convex function greater than or equal to the quadratic function is constructed, regardless of the sign of the coefficient in the quadratic term. The developed lemma can also be degenerated into the existing quadratic function negative-determination (QFND) lemma and relaxed QFND lemma respectively, by setting two adjustable parameters and two free variables as some particular values. Moreover, for a linear system with time-varying delays, a relaxed stability criterion is established via our developed lemma, together with the quivalent reciprocal combination technique and the Bessel-Legendre inequality. As a result, the conservatism can be reduced via the proposed approach in the context of constructing Lyapunov-Krasovskii functionals for the stability analysis of linear time-varying delay systems. Finally, the superiority of our results is illustrated through three numerical examples.
- Equivalent reciprocal combination technique,
- quadratic function convex approximation approach,
- stability,
- timevarying delay

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References

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A novel quadratic convex function is constructed to approximate the quadratic function induced by LKF derivative, regardless of the sign of the coefficient in the quadratic term. As a result, the quadratic function convex approximation lemma is innovatively put forward, and other redundant conditions cannot be produced. When the two adjustable parameters and two free variables are set as particular values, our developed lemma can also be degenerated into the existing quadratic function negative determination (QFND) lemma and relaxed QFND lemma, respectively
To estimate the derivative of the constructed LKF, equivalent reciprocal convex combination (ERCC) technique in our previous work combining the B-L inequality is utilized to obtain the tighter lower bound. ERCC technique is able to solve the reciprocal convex combination problem equivalently and directly without the Schur complement and also the RCC condition is removed, which always exists in other results
The relaxed stability conditions for linear systems with time-varying delays can be obtained by combining our developed quadratic function convex approximation lemma, ERCC technique and the B-L inequality. The conservatism of stability conditions is reduced fundamentally, which is more general than the existing results. B-L inequality. The conservatism of stability conditions is reduced fundamentally, which is more general than the existing results

Relaxed Stability Criteria for Time-Delay Systems: A Novel Quadratic Function Convex Approximation Approach

doi: 10.1109/JAS.2023.123735

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通讯作者: 陈斌, bchen63@163.com

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